Barcelona will allow West Ham to take Gomes for free if they can guarantee he will play 70 per cent of their games.
The 24-year-old has struggled to break into the starting XI at the Camp Nou since his arrival from Valencia last summer.
Meanwhile, the Hammers have had a loan bid rejected from Everton for winger Kevin Mirallas.
Slaven Bilic is keen to bolster his midfield options before the transfer deadline closes on Thursday evening.
Everton manager Ronald Koeman recently questioned the Belgian's attitude, which sparked rumours he could be on his with out of the club.
One player who is trying to force his way out of West Ham is Diafra Sakho. The striker completed a medical with French club Rennes but the Hammers have now blocked the transfer.
A fee of £9m had been agreed between the two clubs, but Bilic wants to keep Sakho as cover.